8

The notion of Hilbert space comes from Hilbert's theory of integral equations. Of course, it was partially motivated by physics, by the theory of oscillations in classical mechanics, but this theory was developed much earlier than quantum mechanics: the main work Grundzuge einer allgemeinen Theorie der linearen Intergalgleichungen (Foundations of the general ...


6

This is called the spectral inclusion theorem. Toeplitz's 1918 paper Das algebraische Analogon zu einem Satze von Fejér already has it for finite dimensional operators as Satz 4. This was before the language of operators and Hilbert spaces introduced by von Neumann in 1927-29, see Highlights in the History of Spectral Theory by Steen, so it is phrased in ...


6

From Steen’s paper mentioned in a very similar MO question just yesterday: Hilbert himself was astonished that the spectra of his quadratic forms should come to be interpreted as atomic spectra. “I developed my theory of infinitely many variables from purely mathematical interests, and even called it ‘spectral analysis’ without any presentiment that it ...


5

Good sources on the history of fixed point theorems are Park, Ninety Years of the Brouwer Fixed Point Theorem and Kumar, A Short Survey of the Development of Fixed Point Theory. According to both, early versions of fixed point theorem concerned self-maps, from a ball or some other set to itself. The first version for non-self maps is in Rothe's Zur Theorie ...


3

The original version of the dominated convergence, from which the monotone convergence trivially follows assuming that the limit is Lebesgue integrable, was published by Lebesgue in Leçons sur l'Intégration et la Recherche des Fonctions Primitives (1904). This is a compilation of his lectures at Collège de France over the preceeding five years. In Sopra l'...


3

It is existence and uniqueness question for ordinary differential equations. When I was a student (in 1970s) Lipschitz functions were not omnipresent in Analysis. The only context where this name appeared (in undergraduate curriculum) was existence and uniqueness theorem for ODE. And this was apparently his original motivation, as the reference in the ...


1

It seems the only firm fact about the origin of the problem is that it is discussed for the first time in print in 1969 in Rosenthal's On quasi-complemented subspaces of Banach spaces, without attribution to Banach or Mazur. The attribution to Mazur appears in Ferrando--Kakol--Lopez-Pellicer--Sliwa paper On the separable quotient problem for Banach spaces ...


Only top voted, non community-wiki answers of a minimum length are eligible